Geodesic
Decay for solutions of the wave equation on Kerr exterior spacetimes III: The full subextremalcase $|a| M$
Mihalis Dafermos1 ; Igor Rodnianski2 ; Yakov Shlapentokh-Rothman2
1 University of Cambridge, Department of Pure Mathematics and Mathematical Statistics, Cambridge, United Kingdom and Princeton University, Princeton, NJ
2 Princeton University, Princeton, NJ
Annals of mathematics, Tome 183 (2016) no. 3, pp. 787-913.

Voir la notice de l'article provenant de la source Annals of Mathematics website

This paper concludes the series begun in [M. Dafermos and I. Rodnianski, Decay for solutions of the wave equation on Kerr exterior spacetimes I–II: the cases $|a| \ll M$ or axisymmetry, arXiv:1010.5132], providing the complete proof of definitive boundedness and decay results for the scalar wave equation on Kerr backgrounds in the general subextremal $|a|< M$ case without symmetry assumptions. The essential ideas of the proof (together with explicit constructions of the most difficult multiplier currents) have been announced in our survey [M. Dafermos and I. Rodnianski, The black hole stability problem for linear scalar perturbations, in Proceedings of the 12th Marcel Grossmann Meeting on General Relativity, T. Damour et al. (ed.), World Scientific, Singapore, 2011, pp. 132189, arXiv:1010.5137]. Our proof appeals also to the quantitative mode-stability proven in [Y. Shlapentokh-Rothman, Quantitative Mode Stability for the Wave Equation on the Kerr Spacetime, arXiv:1302.6902, to appear, Ann. Henri Poincaré], together with a streamlined continuity argument in the parameter $a$, appearing here for the first time. While serving as Part III of a series, this paper repeats all necessary notation so that it can be read independently of previous work.
DOI : 10.4007/annals.2016.183.3.2

Mihalis Dafermos 1 ; Igor Rodnianski 2 ; Yakov Shlapentokh-Rothman 2

1 University of Cambridge, Department of Pure Mathematics and Mathematical Statistics, Cambridge, United Kingdom and Princeton University, Princeton, NJ
2 Princeton University, Princeton, NJ 
@article{10_4007_annals_2016_183_3_2,
     author = {Mihalis Dafermos and Igor Rodnianski and Yakov Shlapentokh-Rothman},
     title = {Decay for solutions of the wave equation on {Kerr} exterior spacetimes  {III:} {The} full subextremalcase $|a|  < M$},
     journal = {Annals of mathematics},
     pages = {787--913},
     publisher = {mathdoc},
     volume = {183},
     number = {3},
     year = {2016},
     doi = {10.4007/annals.2016.183.3.2},
     mrnumber = {3488738},
     zbl = {06589409},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.4007/annals.2016.183.3.2/}
}
TY  - JOUR
AU  - Mihalis Dafermos
AU  - Igor Rodnianski
AU  - Yakov Shlapentokh-Rothman
TI  - Decay for solutions of the wave equation on Kerr exterior spacetimes  III: The full subextremalcase $|a|  < M$
JO  - Annals of mathematics
PY  - 2016
SP  - 787
EP  - 913
VL  - 183
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.4007/annals.2016.183.3.2/
DO  - 10.4007/annals.2016.183.3.2
LA  - en
ID  - 10_4007_annals_2016_183_3_2
ER  - 
%0 Journal Article
%A Mihalis Dafermos
%A Igor Rodnianski
%A Yakov Shlapentokh-Rothman
%T Decay for solutions of the wave equation on Kerr exterior spacetimes  III: The full subextremalcase $|a|  < M$
%J Annals of mathematics
%D 2016
%P 787-913
%V 183
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.4007/annals.2016.183.3.2/
%R 10.4007/annals.2016.183.3.2
%G en
%F 10_4007_annals_2016_183_3_2
Mihalis Dafermos; Igor Rodnianski; Yakov Shlapentokh-Rothman. Decay for solutions of the wave equation on Kerr exterior spacetimes  III: The full subextremalcase $|a|  < M$. Annals of mathematics, Tome 183 (2016) no. 3, pp. 787-913. doi : 10.4007/annals.2016.183.3.2. http://geodesic.mathdoc.fr/articles/10.4007/annals.2016.183.3.2/

Cité par Sources :